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I call with small pairs because I think it is profitable. PT shows that it is. I raise with big cards because I think it is profitable. If I were to play against myself, this presents a paradox - one side should be the favorite, so one side must be making an error in playing.

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I am especially intrigued with this part of the OP. This same thing goes through my head often and I feel like I need a better understanding of what do to on either side of this equation. Seems to me like 77 vs AK type matchups should heavily favor the pocket pair. AK will only hit the flop 30% of the time, so it would seem like you should be able to pound away with 77 70% of the time and pick up that pot. Does AK make up for that 70% by being able to represent a high PP? Trying to incorporate the times it's actually 77 vs a higher PP or the times 77 hits a set + the times 77 hits a set and AK hits TPTK just make things too complex for me to think about which type of hand is preferable.